Introduction to finite fields and their applications
Introduction to finite fields and their applications
Matching is as easy as matrix inversion
Combinatorica
Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
SIAM Journal on Computing
Interpolation and approximation of sparse multivariate polynomials over GF(2)
SIAM Journal on Computing
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Designing programs that check their work
Journal of the ACM (JACM)
SIAM Journal on Computing
Reducing randomness via irrational numbers
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Algebraic methods for interactive proof systems
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
IP=PSPACE (interactive proof=polynomial space)
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Nondeterministic exponential time has two-prover interactive protocols
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Probabilistic checking of proofs; a new characterization of NP
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Riemann's hypothesis and tests for primality
Journal of Computer and System Sciences
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Deterministic identity testing for multivariate polynomials
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Query-efficient algorithms for polynomial interpolation over composites
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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We give a simple and new primality testing algorithm by reducing primality testing for number n to testing if a specific univariate identity over Zn holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Zn for any n. The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, e.g., the Schwartz-Zippel test, Chen-Kao and Lewin-Vadhan tests.Our algorithms first transform the input polynomial to a univariate polynomial and then use Chinese remaindering over univariate polynomials to efficiently test if it is zero.